The Quantity Theory of Money: A Definitive Study Guide

Historical Origins of the Quantity Theory of Money (1500s)

• Nicolaus Copernicus and the Value of Coinage (1517):     * In the text Geldlehre [Money and Value], Copernicus identifies that money can lose its value through "excessive abundance."     * He notes that if excessive silver is coined, it heightens people's desire for silver bullion rather than the currency itself.     * The estimation of the coinage vanishes when the coin cannot purchase as much silver as the raw material the money contains.     * The Melting Incentive: Copernicus points out that when the value of the coin falls below the value of its metal content, it becomes advantageous to destroy the coin by melting the silver.     * The Prescription: To restore value, the solution is to cease minting more coinage until it recovers its "par value."

• Martín de Azpilcueta and the School of Salamanca (1556):     * In Comentario resolutorio de cambios [On Exchange], Azpilcueta treats money as an object of exchange similar to any other commodity.     * Supply and Demand: Value is dictated by "abundance" (supply) and "need" (demand).     * Morality and Ethics: His work relates economic principles back to Aristotelian morality.     * Time Value of Money: He articulates the concept that present value exceeds future value (\text{present} > \text{future}), providing a moral justification for interest, referencing the traditions of Aquinas.

• Jean Bodin and the Early Analysis of Inflation (1568):     * In La rponse aux paradoxes de Malestroit, Bodin provides one of the first sophisticated European analyses of inflation, which was largely unknown before the 16th century.     * Confutation of Debasement: He argues against contemporary explanations that blamed inflation solely on debasement (lowering the metal content of coins).     * Identified Causes of Inflation:         * Abundance of Metals: The primary cause is the sudden abundance of precious metals (silver and gold) flowing throughout Europe.         * Monopolies: Market control by single entities drive prices up.         * Scarcity: Specifically, an imbalance where exports exceed imports (\text{export} > \text{import}).         * Luxury Demand: High demand for luxury products.         * Debasement: Mentioned as a contributing factor but not the sole cause.

Early Modern Approaches to Monetary Theory (1600s-1700s)

• John Locke and the Volume of Commerce (1691):     * In Some Considerations of the Consequences of the Lowering of Interest, and Raising the Value of Money, Locke explores the relationship: $M \implies P$.     * Increasing the money supply leads to an increase in price levels.     * Inversely Proportional Values: The value of money is inversely proportional to:         1. Its quantity in circulation.         2. Its speed of circulation, also known as the "velocity of money."         3. The silver or gold content (addressing the effects of debasement).     * Interest Rates: Locke argued against the government lowering the legal rate of interest, viewing the money supply as the driver for interest rates.

• Richard Cantillon and the Transmission Mechanism (1730):     * In Essai Sur La Nature Du Commerce En Gnral, Cantillon inspects the specific mechanisms of price changes.     * Balance of Trade: Surplus in trade leads to an inflow of precious metals, which subsequently causes inflation.     * The Cantillon Effect: Changes in the money supply are not proportional across all sectors. The effect depends on the "recipients of money"; those who receive the new money first (e.g., gold miners or exporters) spend it, raising prices before others receive the new supply.     * Money Substitutes:         * Bank Notes: These can increase the velocity of circulation.         * Fiduciary Media: Confidence in the banking system acts as an equilibrating factor.

• David Hume and the Critique of Mercantilism (1752):     * In Political Discourses. Of money., Hume describes money as the "oil" that facilitates the machine of commerce, rather than the "wheel" of the machine itself.     * Long-Run Neutrality of Money: The nominal amount of money is irrelevant in the long run. If the money supply doubles, prices double, while production and employment remain unaffected.     * Price-Specie-Flow Mechanism: International competitiveness serves as an equilibrating factor to balance money flows.     * Short-Run Real Costs: Inflation can cause short-term disruptions, such as the loss of labor.     * Public Debt: Hume warns against the accumulation of "paper money" versus real physical wealth.

• Adam Smith and the Role of Credit (1776):     * In An Inquiry into the Nature and Causes of the Wealth of Nations, Smith observes that money facilitates the division of labor.     * Categories of Money:         * Commodity-Money: Based on gold or silver; supply is exogenous and supports the neutrality of money.         * Credit: Supply is endogenous. Banks "create" money according to the "needs of trade," a principle known as the "Real Bills" doctrine.

The Bullionist Controversy and Banking Debates (1800-1850)

• Henry Thornton and the Lender of Last Resort (1802):     * Focusing on the financial crises in England (1793-1797) and the resulting loss of confidence in the banking system (country banks).     * In An Inquiry into the Nature and Effects of the Paper Credit of Great Britain, Thornton identifies the Bank of England (BoE) as the "lender of last resort" to solve crises.     * He warns of the risk of "over-issue" of BoE notes.

• David Ricardo and the Bullionist Argument (1810):     * During the suspension of the gold standard (1798-1818), the price of gold rose significantly.     * The Bullionist View: The issuance of banknotes by the BoE drives up the price of bullion and causes inflation. The solution is to restore convertibility of notes to gold.     * The Counter-Argument (Real Bills Doctrine): The BoE only issues bills against genuine commercial transactions, preventing speculative finance. This suggests "reverse causation": income and prices determine the demand for credit, which then determines the supply of credit ($\text{Income/Prices} \implies \text{Demand for Credit} \implies \text{Supply of Credit}$).

• The Banking Debates of the 1840s:     * The Currency School (Lord Overstone, 1837): Argued that paper currency should act exactly like metallic currency. If there is a balance of payments deficit, gold is lost, and the BoE should reduce note issues "pound for pound." This is a "preventive" monetary policy.     * The Banking School (Thomas Tooke, 1857): During depressions and credit shortages, the BoE should expand note issue. This is an "alleviating" policy based on the "doctrine of reflux," where excess notes naturally return to the bank.

• John Stuart Mill and Monetary Disequilibrium (1844):     * Mill identified money as a "store of value."     * Say’s Law Assumption: Assumes no hoarding (all money is spent), meaning money is a "veil" covering the real economy (neutrality).     * Disequilibrium: Short-term crises are caused by misallocation or ill-assorted production. Endogenous crises (Hume) result in an excess demand for money and an excess supply of goods. Credit (Banking school) is essential for speeding up recovery.

Marxian Critique and Mathematical Formulations (1860-1890)

• Karl Marx and Reverse Causation (1867):     * In Das Kapital, Marx distinguishes between the total "stock of money" and "money in circulation."     * Labor Theory of Value: Relative prices are determined by labor. These prices and the velocity of circulation of goods determine how much money is in circulation.     * The Result: $P \implies M$ (Price levels cause the money supply, not vice versa).

• Simon Newcomb and the Flow of Currency (1885):     * Defined the flow of currency: Total monetary flows ($Y$) equals volume of money ($M$) times rapidity of circulation ($V$): $Y = M \times V$.     * Defined societary circulation: Total monetary flows ($Y$) also equals price of goods ($P$) times volume of transactions ($T$): $Y = P \times T$.     * Fund vs. Flow: A "fund" is a quantity of value; a "flow" is a double transfer of ownership.

Neoclassical Formulations (1880-1920)

• Alfred Marshall: The Expenditure Approach (1890):     * Desired cash balances ($M$) are proportional ($k$) to total expenditure ($P \times Y$): $M = k \times P \times Y$.     * Money’s primary link is with expenditure (demand for money).     * Interest Rates: In the long run, gold is the anchor, and rates are determined by the supply/demand of "capital disposal" (funds) and business profitability. In the short run, the market rate ($i$) can deviate from the natural rate ($r$).

• Knut Wicksell: The Cumulative Process (1898):     * Investigated the loanable funds market.     * The Natural Rate ($i^<em>$): The rate determined by real capital supply and demand.      Market Rate ($i$): When banks allow the market rate to deviate from the natural rate ($i \neq i^*$), it leads to changes in the price level ($\Delta P$).

• Irving Fisher: The Equation of Exchange (1911):     * Formula: $M \times V = P \times T$.     * If $V$ and $T$ are fixed, increasing $M$ must increase $P$ proportionately.     * The Adjustment Process: Excess supply of money leads to excess demand for goods, increasing the general price level.     * Fisher’s Law: $\Delta P \implies \Delta i$ (Inflation impacts nominal interest rates).

• Arthur Cecile Pigou: The Cash-Balance Approach (1917):     * Formula: $P = k \times \frac{R}{M}$.     * $R$ represents real resources; $k$ is the proportion held as cash ($k \times R = \text{money demand}$).     * Fluctuations in the demand for cash are driven by interest rates ($\Delta i \implies \Delta k$).

20th Century Critiques and Evolutions

• The Austrian School (Ludwig von Mises, 1912):     * Argued the Quantity Theory is too mechanical.     * Subjective Evaluation: Human action and subjective value determine the value of money.     * Non-neutrality: Expansion of credit has real effects, such as "over-investment," and non-uniform price changes (Cantillon effect).

• The Keynesian Approach (1920-1940):     * Early J.M. Keynes: Accepted the long-run validity of the cash-balance approach.     * Later J.M. Keynes: Focused on the indirect link between money and prices.         * Unemployment (Elastic Supply): $\Delta M \implies \Delta i \implies \Delta \text{investment} \implies \Delta \text{aggregate demand} \implies \Delta Y$ (Output).         * Full Employment (Inelastic Supply): $\Delta M \implies \Delta i \implies \Delta \text{investment} \implies \Delta \text{aggregate demand} \implies \Delta P$ (Prices).

• The Monetarist Approach (Milton Friedman, 1950-1970):     * Emphasized that "money matters" based on empirical evidence.     * Formula: $\Delta M \times \tilde{V} = \Delta P \times \tilde{Y}$.     * Velocity ($V$) is stable. Permanent income/wealth determines money demand.     * Policy Rules: Advocated for the "Friedman rule" (k-Percent Rule), suggesting money supply should grow between $3\%$ and $5\%$ annually.     * Historical Example: Volcker Disinflation (1979-1982) used interest rates ($\Delta i_{cb}$) to control money aggregates ($M1$, $M2$) to impact output and prices.

• The New Classical and New Keynesian Models (1970-2000):     * Robert Lucas Jr. (New Classical): Rational Expectation Hypothesis. Unanticipated money "surprises" affect output ($Y$), while anticipated changes only affect prices ($P$).     * John Taylor (New Keynesian): Shifted focus from money supply instruments to the nominal policy interest rate instrument. Developed the Taylor Rule:         * $i_t = \Delta P_t + r_t^* + a_{\pi} \times (\Delta P_t - \Delta P_t^<em>) + a_{\pi} \times 100 \times \frac{Y_t - \tilde{Y}_t}{\tilde{Y}_t}$.          Includes the "Taylor Principle": increase nominal rates by more than one-for-one in response to inflation.     * Michael Woodford (2003): Introduced NK-DSGE models using micro-foundations. Assumes "sticky prices" (nominal rigidities), ensuring that interest rate changes have a strong response in real output ($Y$) and a weak response in prices ($P$) in the short run.